Problem: Simplify; express your answer in exponential form. Assume $a\neq 0, z\neq 0$. $\dfrac{{(a)^{5}}}{{(a^{-4}z^{-5})^{5}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${a}$ to the exponent ${5}$ . Now ${1 \times 5 = 5}$ , so ${(a)^{5} = a^{5}}$ In the denominator, we can use the distributive property of exponents. ${(a^{-4}z^{-5})^{5} = (a^{-4})^{5}(z^{-5})^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(a)^{5}}}{{(a^{-4}z^{-5})^{5}}} = \dfrac{{a^{5}}}{{a^{-20}z^{-25}}}$ Break up the equation by variable and simplify. $\dfrac{{a^{5}}}{{a^{-20}z^{-25}}} = \dfrac{{a^{5}}}{{a^{-20}}} \cdot \dfrac{{1}}{{z^{-25}}} = a^{{5} - {(-20)}} \cdot z^{- {(-25)}} = a^{25}z^{25}$.